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simplex[convexhull] - find convex hull enclosing the given points
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Calling Sequence
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convexhull(P)
convexhull(P, output=area)
convexhull(P, output=hull)
convexhull(P, output=plot)
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Parameters
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P
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list or set of points in 2 dimensions
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Description
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The command convexhull(P) returns a list of points defining the convex hull of the points in P in counter-clockwise order.
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Every point in P must be a list of an x and y coordinate, both of which must be numbers (of type numeric).
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If the option output=area is specified, the area of the convex hull of the points is returned.
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If the option output=hull is specified, the convex hull is is returned as a list of points. This is the default return value.
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If the option output=plot is specified, a plot of the points and the convex hull is returned.
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Multiple outputs can be specified, for example, output=[hull,area] returns a sequence of two values.
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An  algorithm computing tangents of pairs of points is used.
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For a slightly more geometrical interpretation of the same command, see geometry[convexhull]. The points input and output are geometric points, and the output is considered to be a convex polygon.
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The command with(simplex,convexhull) allows the use of the abbreviated form of this command.
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Examples
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![P := {[0, 0], [1, 0], [1, 1], [1, 1/2], [2, 0], [1/2, 1/2]}](/support/helpjp/helpview.aspx?si=6476/file04444/math99.png)
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![P := {[0, 0], [1, 0], [1, 1], [1, 1/2], [2, 0], [1/2, 1/2]}](/support/helpjp/helpview.aspx?si=6476/file04444/math102.png)
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![[[0, 0], [2, 0], [1, 1]]](/support/helpjp/helpview.aspx?si=6476/file04444/math109.png)
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![H, A := convexhull(P, output = [hull, area])](/support/helpjp/helpview.aspx?si=6476/file04444/math120.png)
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![H, A := [[0, 0], [2, 0], [1, 1]], 1](/support/helpjp/helpview.aspx?si=6476/file04444/math123.png)
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Execute the following to get a plot of the points and the convex hull.
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This creates 50 points uniformly distributed at random on [0,1).
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U01 := proc() Float( R(), -10 ) end proc:
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![P := {seq([U01(), U01()], i = 1 .. 50)}](/support/helpjp/helpview.aspx?si=6476/file04444/math143.png)
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Execute the following to get a plot of the points and the convex hull.
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Download Help Document
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